Abstract
We study quantum corrections to holographic entanglement entropy in AdS_33/CFT_22; these are given by the bulk entanglement entropy across the Ryu-Takayanagi surface for all fields in the effective gravitational theory. We consider bulk U(1)U(1) gauge fields and gravitons, whose dynamics in AdS_33 are governed by Chern-Simons terms and are therefore topological. In this case the relevant Hilbert space is that of the edge excitations. A novelty of the holographic construction is that such modes live not only on the bulk entanglement cut but also on the AdS boundary. We describe the interplay of these excitations and provide an explicit map to the appropriate extended Hilbert space. We compute the bulk entanglement entropy for the CFT vacuum state and find that the effect of the bulk entanglement entropy is to renormalize the relation between the effective holographic central charge and Newton’s constant. We also consider excited states obtained by acting with the U(1)U(1) current on the vacuum, and compute the difference in bulk entanglement entropy between these states and the vacuum. We compute this UV-finite difference both in the bulk and in the CFT finding a perfect agreement.
Highlights
We give an explicit map to the extended Hilbert space which is suitable for topological bulk theories
M : H → H ⊗ H, |ψ〉 → |ψE〉 = ci j |Ei〉 ⊗ |Ej〉, ij for coefficients ci j that we compute and which depend on the original choice of state for the full theory. This computation is simplest when the UV regulator is picked such that entanglement cut degrees of freedom and the physical boundary degrees of freedom are the same, along with a transparent boundary condition at the junction; relaxing these assumptions requires a more involved computation
We find that the bulk entanglement entropy is a sum of two terms, both of which effectively renormalize the relation between the central charge of the holographic CFT and GN
Summary
Understanding the entanglement structure of quantum systems has led to profound results in many areas of physics, going from the characterization of topological phases of matter [1, 2], to monoticity theorems for the central charges [3,4,5] and proofs of energy conditions [6, 7] in quantum field theory. If we make an entanglement cut in order to compute an entanglement entropy, the “same” gapless modes make an appearance at the non-physical entangling surface, as a particular realization of the edge degrees of freedom required to restore gauge invariance In this case one can imagine that the entangling edge degrees of freedom are gapless, and the powerful techniques of conformal field theory can be used to understand their contribution to the entanglement entropy [26]. To the best of our knowledge, such a geometry has not been considered before in the rich literature on entanglement entropy in Chern-Simons theory (see for example [27,28,29,30,31] and references therein) We will study this issue carefully and describe the interaction of the modes living on the fictitious entanglement cut with the modes living on the actual physical boundary of the system. Our work addresses in the context of a gapless edge theory issues similar to those discussed for a gapped edge theory in [34, 35]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
